Many applications include integrated circuits that are powered by power supplies having voltage regulation. Some regulators (such as direct-current-to-direct-current regulators) include undershoot reduction circuitry to achieve regulation of power supply outputs. For example, when the voltage of a power supply output falls below a certain reference voltage, the undershoot reduction circuitry turns on a nonlinear control fast control loop for applying power to raise the voltage of a power supply output. The nonlinear fast control loop is turned off by the undershoot reduction circuitry after the output voltage rises above the reference voltage plus a hysteresis value of the comparator used. This approach often results in an overshoot of the output voltage due to hysteresis and extra energy dissipated in the inductor that is part of the power supply output LC filter. The overshoot problem is compounded in multiphase regulators where more than one such regulated phase is turned on in response to increased load demands.